LONDON (Reuters) - Britain's response on Wednesday to the nerve agent attack on a Russian double agent in southern England does not go far enough and senior Kremlin figures should be targeted with sanctions, the widow of a Russian dissident murdered in London said.

Prime Minister Theresa May told parliament Britain would expel 23 Russian diplomats and freeze Russian state assets wherever there was evidence of a threat as part of measures against Moscow which she blames for the poisoning of Sergei Skripal.

Russia denies any involvement in the March 4 attack on Skripal, 66, and his daughter Yulia, 33, who are both critically ill in hospital, and has accused Britain of unjustified action.

"I think something more should be done. It's not enough," Marina Litvinenko told Reuters in an interview. Her husband Alexander, a former KGB agent, was murdered with the rare radioactive isotope polonium in London in 2006.

"Even though (the reaction) is stronger than it was in (the) case of my husband, it is still not enough."

British Foreign Secretary Boris Johnson is among those who have linked the Skirpal case to that of Litvinenko, a fierce critic of Russian President Vladimir Putin.

A public inquiry in 2016 concluded Litvinenko's murder was carried out by two Russians, one of them a former KGB bodyguard who became a member of the Russian parliament, as part of an operation probably ordered by Putin, allegations Moscow rejects.

After that inquiry, Britain expelled four diplomats and May told lawmakers that this time the response needed to be firmer. While Marina Litvinenko said the reaction had been faster and more direct than two years ago, it was not tough enough.

"You don't need to play with the same rules as Putin, because you'll never win," she told Reuters. "But you don't need to show you're soft and you are accepting everything that happened in your country even after what happened to my husband.

"You need to be more serious and (do) something that maybe Putin doesn't expect."

She said Britain should look at wider and bigger personal sanctions beyond those in the U.S. Magnitsky Act which imposed visa bans and asset freezes on Russian officials.

"It's very important to make severe targeted sanctions," she said, adding that sanctions against the Russian state would be portrayed as an attack on ordinary Russians.

She had to battle with the British authorities to hold the public inquiry into her husband's death which May - then interior minister - had initially ruled out as Britain sought better relations with Russia.

"They tried to protect this relationship between Russia and (the) UK. But Russia's president and these people who are in power in Russia did not accept it. It was softness, even weakness," she said.

She hopes Britain will have learned and May's personal involvement in her husband's case will have hardened her resolve.

"I believe she (...) understands (better) who Mr Putin is," she said.

She said other Russian dissidents living in Britain still did not feel very secure and it was hard not to see the death in London on Monday of another Putin critic, Nikolai Glushkov, 68, as suspicious.

Counter-terrorism police are now investigating his death although they said it was not thought to be linked to the attack on the Skripals.

She said it was hard to accept that Glushkov's death was only due to natural causes.